68 citations · 246 across the 15 of their papers we have counts for
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On Rings of Differential Rota-Baxter Operators
Xing Gao, Li Guo, Markus Rosenkranz
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying th…
Free integro-differential algebras and Gröbner-Shirshov bases
Xing Gao, Li Guo, Markus Rosenkranz
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative an…
Constructions of free commutative integro-differential algebras
Xing Gao, Li Guo
In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras b…
On Integro-Differential Algebras
Li Guo, Georg Regensburger, Markus Rosenkranz
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-…
Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formula
Li Guo, Fang Li
This article studies the Lie algebra of derivations on the path algebra of a quiver and the Lie algebra on the first Hochschild cohomology group . We r…
Algebraic Birkhoff decomposition and its applications
Li Guo
Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial a…
Operated semigroups, Motzkin paths and rooted trees
Li Guo
Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an…
Free Rota-Baxter algebras and rooted trees
Kurusch Ebrahimi-Fard, Li Guo
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota-Baxter relation, that generalizes the integration…
Coherent Unit Actions on Operads and Hopf Algebras
Kurusch Ebrahimi-Fard, Li Guo
Coherent unit actions on a binary, quadratic operad were introduced by Loday and were shown by him to give Hopf algebra structures on the free algebras when the operad is also regu…